Mathematical issues

Reading through von Neumann's book (page 47 onwards) games have taken a more mathematocal approach:
If game G has n players. Then for each player there will be a number of moves M1, M2,...,Mv .
For each move there would also exist alternates for moves a(1), a(2),...a(v).
These vary according to the moves or strategies being chosen.

Then comes a second scenario of a game of Poker P. The moves being played will differ is cheating is involved, one player known the moves or cards of the other players, OR if nobody is cheating.